Friday, May 12, 2017

# Sebastien Vasey Receives Guy C. Berry Graduate Student Research Award

Sebastien Vasey, a Ph.D. candidate in the Department of Mathematical Sciences, has been named the recipient of the Guy C. Berry Graduate Student Research Award.

Vasey conducts research in a branch of mathematical logic called model theory, focusing on classification theory for abstract elementary classes (AECs). Working under the direction of Professor of Mathematical Sciences Rami Grossberg, Vasey has solved cases of one of the most important problems in model theory — Shelah’s Categoricity Conjecture.

The theory of AECs, which Vasey focuses on, was initiated in the late 1970s by Saharon Shelah, emeritus professor of mathematics at the Hebrew University of Jerusalem and a distinguished visiting professor at Rutgers University. His goal was to extend the model theory of first order logic to a much broader class of logics. Shelah conjectured that Morley’s theorem, one of the central results in the model theory of first-order logic, extends in a natural way to all AECs. He believed that an AEC that is categorical in one high-enough cardinal would be categorical in all high-enough cardinals. This statement is now known as Shelah's Categoricity Conjecture. Mathematicians believe that tools developed to resolve the conjecture will also be useful in other fields of mathematics, including algebra and geometry.

After 40 years and thousands of pages of partial approximations, Shelah’s conjecture remains open. Grossberg and his former Ph.D. students Monica VanDieren and Will Boney had developed and extended an alternative strategy to Shelah's approach. Vasey combined recent work of Shelah with the Grossberg group’s alternative strategy to obtain a proof of Shelah’s eventual categoricity conjecture for universal classes, a general family of AECs. The result is the best approximation of the conjecture to date and also produces machinery that is useful for other applications in model theory.

“Vasey is a mature mathematician, both in terms of significance of mathematical results and in publication record. He is already a major, leading figure in a field that very few people have managed to enter in the last 40 years,” said Grossberg, Vasey’s Ph.D. advisor.

To date, Vasey has submitted 23 papers for publication. Seventeen of his papers have been accepted by refereed journals, including Selecta Mathematica, a top mathematics journal. Vasey has successfully defended his Ph.D. thesis and plans to go to Harvard under a Benjamin Peirce Fellowship. There he will further develop the theory that led to his proof of the categoricity conjecture for universal classes and the dividing lines around it.

By: Emily Payne, epayne@andrew.cmu.edu, 412-268-4859